When it comes to Pi, it is proven that EVERY finite sequence of ziphers occurs in decimal representation of Pi. And therefore, every finite sequence occurs infinitely many times, because every finite sequence is subsequence of arbitrarily many longer sequences, which also occur there. So for example, in Pi we can have sequence of '0123456789' repeated 10^(24^(576^(21860))) times!!! But it does not happen for any irrational real number.
Can I ask You to do a 10 second favour for me? Please + that post of SchamanGerbert - he was organising chess tournaments, but the future is not bright for that: https://steemit.com/chess/@schamangerbert/steem-chess-tournament-february-01-the-winner-is-eniolw-last-edition